Pith Number

pith:FPEVKMNQ

pith:2026:FPEVKMNQJ2SP4IBZ6ZSNXVQO74

not attested not anchored not stored refs pending

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise

Jiayu Zhang, Tianyi Lin

arxiv:2605.18528 v1 · 2026-05-18 · math.OC · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FPEVKMNQJ2SP4IBZ6ZSNXVQO74}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-20T00:06:06.039402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bc95531b04ea4fe2039f664dbd60eff2d7a043626480bad08a8c0cb12515212

Aliases

arxiv: 2605.18528 · arxiv_version: 2605.18528v1 · doi: 10.48550/arxiv.2605.18528 · pith_short_12: FPEVKMNQJ2SP · pith_short_16: FPEVKMNQJ2SP4IBZ · pith_short_8: FPEVKMNQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FPEVKMNQJ2SP4IBZ6ZSNXVQO74 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2bc95531b04ea4fe2039f664dbd60eff2d7a043626480bad08a8c0cb12515212

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d728048b5cc09b4776ca9b425d7beeda56b1ef055faf0f1a69256a6e3380152b",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-18T15:13:18Z",
    "title_canon_sha256": "8a841b4bd237e91e1fafa7aedf21a30e9cbbf265998ae3f62b409b94ecc41d51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18528",
    "kind": "arxiv",
    "version": 1
  }
}